##
Introduction

The mathematics degree at UMass provides the student with broad exposure to the most important themes in mathematics and statistics, while allowing the student to specialize in one or more areas. Our rigorous mathematical and statistical training, coupled with exposure to computing paradigms (whether in Java, Python, MATLAB, R, and/or SAS), has provided our majors with increasing success in the job and graduate school marketplace.

While completing the Mathematics B.S. and B.A., students will develop effective thinking and communication skills, learn to link applications and theory, learn to use technological tools, and develop mathematical independence and experience open-ended inquiry. Students will also have the opportunity to gain experience with computational, algorithmic, and statistical thinking.

In recent years, primary math majors have taken jobs at companies ranging from British Aerospace to Raytheon to Microsoft to Optum to MassMutual to Willis Towers Watson, have begun Master's programs including at WPI, Columbia, Northeastern, and Harvard in a range of fields such as Applied Math, Statistics, Biostatistics, Computer Science, Data Science, Actuarial Science, Education and Business, and have started PhD programs at UC Berkeley, Michigan, NYU, UC Santa Barbara, Columbia, and Boston University in Pure Math, Biostatistics, and Statistics. Our second majors have used the math degree to amplify their training in such subjects as Economics, Physics, Computer Science, Finance, Engineering, Chemistry, Political Science and Psychology.

For information about joining the major, please see our Advising Page.

##
Concentrations within the Major

The department offers seven **concentrations **as part of the mathematics degree, which allow the student to specialize in one of six focused areas, or create their own: Actuarial, Applied Math, Individual, Math Computing, Pure Math, Statistics and Data Science, and Teaching. Students are expected to choose a concentration by the middle of their second semester, but are encouraged to do so earlier. Please email Jacob Lagerstrom to choose or change your concentration.

##
Core Requirements for all Majors

**Differential and integral calculus:**MATH 131 and 132, with a grade of C or better in Math 132**Multivariable calculus and linear algebra:**MATH 233 and 235**Introduction to abstract mathematics:**MATH 300 or COMPSCI 250. This requirement may be waived by the Chief Undergraduate Advisor, Sohrab Shahshahani, for students who have taken advanced math coursework elsewhere in abstract algebra, real analysis, or number theory.**Computer programming:**CICS 110 OR INFO 190S OR COMPSCI 121 or equivalent**Writing in mathematics:**MATH 370**Integrative Experience (IE) course.**The following courses satisfy the IE requirement: Math 455, Math 456, Math 475, Stat 525, Stat 494CI**.**All IE courses count toward either required major courses or upper level major electives. In other words, this requirement does not require additional coursework to be completed.- Completion of the requirements of one of the following concentrations: Actuarial, Applied, Individual, Mathematical Computing, Pure, Statistics and Data Science, Teaching.

##
Grade Requirements

- All courses used to satisfy these requirements must be completed with a passing grade (D or higher) and cannot be taken Pass/Fail.
- The overall GPA of all courses taken to satisfy the requirements for the major (averaged over all such courses taken) must be at least 2.0.
- Students will need to
**earn a grade of C or better in Math 132 before taking certain courses at the 300 level or higher**.

## Update on Math 425

Following the Spring 2021 semester, the department will stop offering Math 425. This course is required for Applied, Pure and Statistics concentrations. See below for the information about which courses can substitute for Math 425. **All replacement courses must be 3 or more credits and cannot be used for another requirement in the concentration.** Also note that we will go into Spire and make the substitution course count; it will not happen automatically.

##
Concentrations and their requirements

Mathematics majors must choose one of the following **concentrations **before registering for their third semester of classes. Courses from outside the department may be used to satisfy the concentration requirements: a list of accepted University courses is available here. The Chief Undergraduate Advisor may approve other courses taken outside the department or at another university, but this must be done before the student enrolls in them.

**Note: ** If you are pursuing a minor in another department (e.g., Econ or CS), please check their implementation of the multiple credential policy to see if courses you are considering using for both the math major and their minor are eligible to fulfill both requirements simultaneously.

### Actuarial Concentration

The Actuarial Concentration prepares the student for a career in the actuarial sciences. Requirements:

**VEE requirements outside the department**: ECON 103 (or Res-Econ 102), ECON 104, and FINANCE 301.**Accounting 221**is now a VEE, but it is not yet a requirement of the concentration. Students are encouraged to take Acct 221.**Probability and statistics**: STAT 315 (was Stat 515) and STAT 516**Linear Regression:**Stat 525. Stat 525 is an IE course.**Exam preparation**: MATH 437 or MATH 536**Mathematics of finance**: MATH 537- Three of the following courses: MATH 331, MATH 405/397C, MATH 425, MATH 456, MATH 523H, MATH 545, Math 548/597U, MATH 551, STAT 526, STAT 535, or an appropriate course outside the department such as FINANCE 422, Econ 309, Econ 452, or Public Health 460. For other substitutions see the approved outside course list. Only one course outside the department is permitted.

See the Actuarial Sciences webpage for further details on this concentration.

### Applied Mathematics Concentration

The Applied Mathematics Concentration prepares the student for applied mathematics positions in industry or government. Requirements:

**Advanced multivariate calculus:**MATH 425- The following courses (
**if not used elsewhere**) will substitute for 425: Math 405/397C, 421, 522/597F, 523H, 524, 532H, 534H, 548/597U, 552, Stat 516 or 525

- The following courses (
**Differential equations:**MATH 331**Linear algebra for applied mathematics:**MATH 545**Introduction to scientific computing:**MATH 551- One of the following courses: MATH 456, MATH 532, MATH 534, MATH 552. MATH 456 is the IE course for this concentration.
- Three electives: three additional Math or Stats courses numbered 400 or higher (
**except Stat 501)**. Stat 315 can count as one of the electives. - Students are permitted (and encouraged) to take one of the electives outside the department. Approved courses include MIE 379, Public Health 460, and Econ 309. For other outside courses see the approved outside course list.

### Individually Designed Concentration

The individually designed concentration permits students, in consultation with the Chief Undergraduate Advisor, to design their own concentration so as to explore a theme in mathematics or statistics or to investigate connections between the mathematical sciences and another field. An individual concentration includes the core requirements above plus eight courses numbered 400 or above, of at least three credits each. In practice, very few students choose this option since most of the other concentrations have enough flexibility, including three open electives in both the Applied Math and Statistics and Data Science concentrations. Generally, the individual concentration will only be approved for students with a single major to allow them to gain exposure to multiple disciplines, rather than as a mechanism to add a second major in math using coursework from a primary major. Students also have the option to do BDIC if they are interested in a field that utitilizes mathematics, statistics, or data science.

### Mathematical Computing Concentration

The Mathematical Computing Concentration prepares the student for careers that require both knowledge of advanced mathematics and knowledge of computer science. Requirements:

**Object-Oriented Programming:**CICS 160. This course is a pre-requisite for CS 250 and CICS 210.**Data Structures:**CICS 210 (or CompSci 187). This course is a prerequisite for CS 311.**Abstract algebra:**MATH 411**Probability:**STAT 315 (was Stat 515)**Intro Scientific Computing:**MATH 551**Algorithms:**COMPSCI 311. The pre-requisites of this course are: CICS 210 (or COMPSCI 187) and either COMPSCI 250 or MATH 455, all with a grade of C or better.- COMPSCI 501 or Math 513/COMPSCI 575. CompSci 501 is offered in Spring semesters, and the pre-requisite is CS 311 with a grade of C or better. Math 513 is cross-listed with CompSci 575, offered in even Fall semesters, and the pre-requisite is either CS 250 or Math 455 with a grade of B or better.
- Two additional courses from the following list: MATH 331, MATH 412, MATH 456, MATH 471, MATH 545, Math 548/597U, MATH 552, MATH 571 or STAT 516. The IE course on this list is MATH 456.
- CS elective: any 300+ level CS course of 3 credits or more that is not used to satisfy any of the previous requirements.

### Pure Mathematics Concentration

The Pure Mathematics Concentration gives students exposure to the core mathematics subjects and prepares students for graduate study in mathematics. Requirements:

**Abstract algebra:**MATH 411**Complex variables:**MATH 421**Real Analysis:**MATH 523H- Advanced Coursework in Analysis, Geometry or Algebra. Two courses from Math 425, Math 522/597F, Math 524, Math 412, Math 481/497K (Knot Theory), Math 557, Math 563H.
- One
**applied mathematics**course either chosen from the following list or another course with sufficient applied mathematical content approved by the Chief Undergraduate Advisor: MATH 331, MATH 456, MATH 532, MATH 534, MATH 551, MATH 552, STAT 516 - Two additional courses numbered 400 or higher (
**except Stat 501**). Stat 315 can also count as one of the electives. Most students will select one of these to be MATH 455 to satisfy the IE requirement. One may be a course from the approved outside course list.

### Statistics and Data Science Concentration

The Statistics and Data Science Concentration prepares the student for a career as a statistician or a data scientist or for graduate study in statistics or biostatistics. Requirements:

**Advanced multivariate calculus:**MATH 425- The following courses
**(if not used elsewhere)**will substitute for 425: Math 523H or 548/597U; Stat 310/297F, 526, 535 or any Stat course above 535; Public Health courses at the 390 level or higher (e.g., PH 390R will count).**Replacement courses must be 3 or more credits.**

- The following courses
**Advanced Algebra:**MATH 545 or 411**Probability and statistics:**STAT 315 (was Stat 515) and STAT 516- One of the following courses: STAT 525 or STAT 526. The IE course on this list is STAT 525.
- Three electives: three additional Math or Stats courses numbered 390 or higher (or MATH 331).
**Note: Stat 501 cannot be used for this list.** - Students are permitted (and encouraged) to take one of the electives outside the department. Approved courses include Public Health 460 or 490Z, Econ 309 or 452, and MIE 379. For other approved courses, see the outside course list.

### Teaching Concentration

The Teaching Concentration provides the student with the knowledge of mathematics and statistics for teaching at the secondary school level.

**Abstract algebra:**MATH 411 or 490A**Mathematical modeling:**MATH 331 or MATH 456**Discrete/finite mathematics:**MATH 455 (an IE course)**Geometry:**MATH 461**Probability and statistics:**Either STAT 501 followed by STAT 315 (was Stat 515) or STAT 315/515 followed by STAT 516**Use of technology:**MATH 471- One additional course numbered 400 or higher. (MATH 475, History of Math, is recommended since it is an education school requirement).

- Undergraduate Overview
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